FOREIGN KEY (DOGSHOWID) REFERENCES CLASSMATE.CH09DOGSHOW(DOGSHOWID) -> as you didn't name it, Oracle created a name for you. It is one of the "R" constraint type (R as referential integrity), SYS_C00...

Therefore, you should have dropped SYS_C00... constraint, not DOGSHOWID. But - which one of SYS_C00...? In order to find that out, broaden previous query so that you'd see table and column names, such as

It is not mandatory to use those table aliases now, run the query and post the result.
By checking the result you can drop the constraint with column_name value as DOGSHOWID then again create a new constraint with ON DELETE CASCADE option.